It's an early S&W pre-model 14, K-38 Masterpiece (sometimes called "Target Masterpiece"). Carefully remove the stocks and you will find the full serial number stamped on the butt, with a letter prefix, "K".
Or you may find it stamped on the bottom of the barrel, above the ejector rod. Swing out the cylinder to see it.
Post the serial number and it can be more closely dated, or for a $50 search fee the exact date it was shipped from the factory, along with other information can be obtained fom the maker.